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Random Matrix Models and Nonparametric Method for Uncertainty Quantification

  • Christian Soize
Reference work entry

Abstract

This chapter deals with the fundamental mathematical tools and the associated computational aspects for constructing the stochastic models of random matrices that appear in the nonparametric method of uncertainties and in the random constitutive equations for multiscale stochastic modeling of heterogeneous materials. The explicit construction of ensembles of random matrices but also the presentation of numerical tools for constructing general ensembles of random matrices are presented and can be used for high stochastic dimension. The developments presented are illustrated for the nonparametric method for multiscale stochastic modeling of heterogeneous linear elastic materials and for the nonparametric stochastic models of uncertainties in computational structural dynamics.

Keywords

Random matrix Symmetric random matrix Positive-definite random matrix Nonparametric uncertainty Nonparametric method for uncertainty quantification Random vector Maximum entropy principle Non-Gaussian Generator Random elastic medium Uncertainty quantification in linear structural dynamics Uncertainty quantification in nonlinear structural dynamics Parametric-nonparametric uncertainties Identification Inverse problem Statistical inverse problem 

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© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Laboratoire Modélisation et Simulation Multi Echelle (MSME)Université Paris-EstMarne-la-ValleeFrance

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